Revealing the effect of external applied potential on the reaction mechanism and product selectivity is of great significance in electrochemical studies. In this work, the grand canonical density functional theory method was applied to simulate the explicit electrocatalytic process of oxygen evolution reaction and electrochemical ozone production due to the O3 product sensitivity toward the applied potential. Over the Pt/Pd single atom embedded on B/N co-doped graphene (Pt/Pd-BNC) surface, crossover points of O2/O3 selectivity inversion were predicted to be 1.33 and 0.89 V vs standard hydrogen electrode, which were also consistent with the previous experimental results. An in-depth analysis of the energetic terms in the reaction free energies also found the considerable impact of the applied potential on the Helmholtz free energy term, with optimal potential predicted for the key elementary steps, and linear correlations between electrode potential (U) and reaction free energy were found for each elementary step. This study offers extensive knowledge on the potential effect on the O2/O3 selective formation on two-dimensional anode surfaces and provides new insights for investigating the reactivity/selectivity on electrode surfaces in real reaction conditions.